Square Root of 1936

The square root is the inverse of the square of a number. 1936 is a perfect square. The square root of 1936 is expressed in both radical and exponential form. In the radical form, it is expressed as √1936, whereas (1936)^(1/2) in the exponential form. √1936 = 44, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:

• Prime factorization method

• Long division method

• Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 1936 is broken down into its prime factors.

Step 1: Finding the prime factors of 1936 Breaking it down, we get 2 x 2 x 2 x 2 x 11 x 11: 2^4 x 11^2

Step 2: Now we have found the prime factors of 1936. The second step is to make pairs of those prime factors. Since 1936 is a perfect square, we can pair the factors. Thus, √(2^4 x 11^2) = 2^2 x 11 = 44.

The long division method is particularly used for non-perfect square numbers, but it can also verify the square root of perfect squares. Let us learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1936, we need to group it as 36 and 19.

Step 2: Now we need to find a number whose square is less than or equal to 19. We can say '4', because 4 x 4 = 16, which is less than 19. Now the quotient is 4, after subtracting 19 - 16, the remainder is 3.

Step 3: Bring down 36 to make the new dividend 336.

Step 4: Double the quotient and use it as the new divisor. So, 8_ is the new divisor.

Step 5: Find a digit for the blank in '8_' such that when multiplied, the result is less than or equal to 336. In this case, 84 x 4 = 336.

Step 6: Subtract 336 - 336 = 0. Since the remainder is 0 and the quotient is 44.

The square root of 1936 is 44.

The approximation method is useful for finding square roots, but since 1936 is a perfect square, we can verify it using nearby perfect squares.

Step 1: Identify the perfect squares closest to 1936. The perfect square less than 1936 is 1836, and the perfect square greater than 1936 is 2025. √1936 is between √1836 and √2025.

Step 2: √1836 is approximately 43, and √2025 is 45. Since 1936 is a perfect square, it falls exactly at 44.

• Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.

• Rational number: A rational number can be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A number that is the square of an integer. Example: 1936 is a perfect square because it is 44^2.

• Prime factorization: The expression of a number as the product of its prime factors.

• Long division method: A method used to find the square root of a number, particularly useful for non-perfect squares.